基于改进粒子群算法的基数受限最优化问题研究  

Research on Cardinality Constrained Optimization Problem Based on Improved Particle Swarm Optimization

作　　者：万春林[1] 张卫 Wan Chunlin;Zhang Wei(School of Economics,Sichuan University,Chengdu 610065,China;School of Economics,Southwest Minzu University,Chengdu 610041,China)

机构地区：[1]四川大学经济学院,成都610065 [2]西南民族大学经济学院,成都610041

出　　处：《统计与决策》2021年第20期20-24,共5页Statistics & Decision

基　　金：国家自然科学基金资助项目(71742004);甘肃省哲学社会科学规划项目(20YB011)。

摘　　要：通过对粒子群算法的粒子和速度施加不同的基数受限方式,文章提出了4种改进粒子群算法,并算法,仅在非常简单的问题中才可迅速达到全局最优解。(2)当受限资产组合数较多时,对粒子速度和位置均施加基数约束的算法(Bound-PSO)更易接近全局最优解;当受限资产组合数较少时,对粒子速度和位置均未施加约束的算法(Unbound-PSO)更易接近全局最优解。(3)Bound-PSO和Unbound-PSO都可以只在同一种粒子群参数组合下接近全局最优解。因此,在实际问题中可同时采用Bound-PSO和Unbound-PSO两种方法进行比较,以此寻找全局最优解。This paper proposes four improved Particle Swarm Optimization(PSO)algorithms by applying different cardinality constrained modes to particle and velocity of PSO,and specifically applies them to Markowitz portfolio optimization with cardinality constrained modes.The findings of the research are as follows:(1)The algorithm that applies a cardinality constraint on the particle position but no speed constraint can quickly reach the global optimal solution only in very simple problems.(2)When the number of constrained asset portfolios is large,the Bound-PSO algorithm that applies cardinality constraints on both velocity and position of particles is more likely to approach the global optimal solution;when the number of constrained asset combinations is small,the Unbound-PSO algorithm that applies no constraints on the velocity and position of particles is more likely to approach the global optimal solution.(3)Both Bound-PSO and Unbound-PSO can approach global optimal solution only under the same particle swarm parameter combination.Therefore,in practical problems,both Bound-PSO and Unbound-PSO methods can be used to compare and find the global optimal solution.

关 键 词：粒子群算法 基数受限 最优化问题 投资组合 

分 类 号：TP18[自动化与计算机技术—控制理论与控制工程] F830.59[自动化与计算机技术—控制科学与工程]